# Dimension preserving resolutions of singularities of Poisson structures

## TL;DR

This paper investigates when Poisson structures can be resolved by symplectic manifolds of the same dimension, providing examples and conditions that determine the existence or non-existence of such resolutions.

## Contribution

It introduces criteria and examples for the (non-)existence of dimension-preserving symplectic resolutions of Poisson structures.

## Key findings

- Examples of Poisson structures with symplectic resolutions.
- Conditions under which such resolutions cannot exist.

## Abstract

Some Poisson structures do admit resolutions by symplectic manifolds of the same dimension. We give examples and simple conditions under which such resolutions can not exist.